Exam 7: Continuous Probability Distributions

{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

If X is a continuous random variable on the interval [0, 10], then P ( X > 5)= P ( X ³ 5).

Suppose you have an F distribution with degrees of freedom 10, 20. a. Find the mean b. Find the variance. c. Find the standard deviation.

Calculus Scores Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.){Calculus Scores Narrative} What is the probability that a randomly selected student will have a score between 80 and 90?

In the standard normal distribution, z _0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

Suppose f(x)equals 1\50 on the interval [0, 50]. a. What is the distribution of X ? b. What does the graph of f(x)look like? c. Find P ( X £ 25) d. Find P ( X ³ 25) e. Find P ( X = 25) f. Find P (0 X g. Find P ( - 3 X h. Find P (0 X

Waiting Time The length of time patients must wait to see a doctor at an emergency room in a large hospital has a uniform distribution between 40 minutes and 3 hours. {Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours?

In its standardized form, the normal distribution:

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What proportion of these batteries will last less than 3,600 hours?

To be a legitimate probability density function, all possible values of f(x)must lie between 0 and 1 (inclusive).

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. {Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

Battery Life A certain brand of batteries has a lifetime that has a normal distribution with a mean of 3,750 hours and a standard deviation of 300 hours. {Battery Life Narrative} What lifetime should the manufacturer advertise for these batteries in order that only 2% of the lamps will wear out before the advertised lifetime?

To find the probability for a uniform random variable you take the ____________________ times the ____________________ of its corresponding rectangle.

The total area under f(x)for a continuous random variable must equal ____________________.

Diet Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 10 pounds and a standard deviation of 5 pounds. {Diet Narrative} If a dieter is selected at random, what is the probability that the dieter lost more than 7.5 pounds?

Checking Accounts A bank has determined that the monthly balances of the checking accounts of its customers are normally distributed with an average balance of $1,200 and a standard deviation of $250. {Checking Accounts Narrative} What proportion of customers have monthly balances between $950 and $1,075?

The expected value of the Student t distribution is zero.

Like that of the Student t distribution, the shape of the chi-squared distribution depends on its number of degrees of freedom.

Which of the following has a mean and variance that depend on degrees of freedom?

The probability density function f(x)for a uniform random variable X defined over the interval [2, 10] is